We study the dynamics of a cantilever beam vibrating between two rigid stops of specified clearance at its free end by performing nonlinear system identification (NSI) based on the correspondence between analytical and empirical slow-flow dynamics. First, we perform empirical mode decomposition (EMD) on the acceleration responses measured at ten, almost evenly-spaced, spanwise positions along the beam, leading to sets of intrinsic modal oscillators governing the vibro-impact dynamics at different time scales. In particular, the EMD analysis can separate nonsmooth effects caused by vibroimpacts of the beam and the rigid stops from the smooth (elastodynamic) response, so that nonlinear modal interactions caused by vibro-impacts can be explored through the remaining smooth components. Then, we establish nonlinear interaction models (NIMs) for the respective intrinsic modal oscillators, determined from the intrinsic mode functions of the EMD, where the NIMs invoke slowly-varying forcing amplitudes that can be computed from empirical slow-flows. By comparing the spatio-temporal variations of the nonlinear modal interactions for the vibro-impact beam and those of the underlying linear model, we demonstrate that vibro-impacts significantly influence the lower frequency modes by introducing spatial modal distortions, whereas the higher frequency modes tend to retain their linear dynamics between impacts. Finally, we demonstrate that the proposed NSI method can extract spatiotemporal nonlinear modes, as further method development moves toward structural health monitoring and damage detection.